The Riemannian gradient descent method under the quotient geometry (RGD (Q)) for the low-rank tensor completion problem is presented in Algorithm REF . Let \(\bar{{\cal X}}_t\)  be the current estimator. RGD (Q) updates \(\bar{{\cal X}}_t\)  along the negative Riemannian gradient direction given in (REF ), followed by retraction.
The step size \(\alpha _t\)  at \(t\) -th iteration is calculated by the standard backtracking line search procedure. For \(t = 0\) , we take \(\alpha _0^{0} = 1\)  as the initial step size. For \(t\ge 1\) , the following Riemannian Barzilai–Borwein (RBB) step size rule [1]} without safeguard will be considered,
\(\alpha _t^0 := \frac{\bar{g}_{\bar{{\cal X}}_t}\left(s_t,s_t\right)}{\left|\bar{g}_{\bar{{\cal X}}_t}\left(s_t,y_t\right)\right|},\) 
